-
1
-
-
0032552250
-
A global optimization method αBB, for general twice-differentiable constrained NLPs - I. Theoretical advances
-
Adjiman C.S., Dallwig S., Floudas C.A., Neumaier A. A global optimization method αBB, for general twice-differentiable constrained NLPs - I. Theoretical advances. Computers and Chemical Engineering 1998, 22(9):1137-1158.
-
(1998)
Computers and Chemical Engineering
, vol.22
, Issue.9
, pp. 1137-1158
-
-
Adjiman, C.S.1
Dallwig, S.2
Floudas, C.A.3
Neumaier, A.4
-
3
-
-
35349028809
-
From taylor series to taylor models
-
American Institute of Physics CP405
-
Berz M. From taylor series to taylor models. Nonlinear problems in accelerator physics 1997, 1-27. American Institute of Physics CP405.
-
(1997)
Nonlinear problems in accelerator physics
, pp. 1-27
-
-
Berz, M.1
-
4
-
-
0000329979
-
Verified integration of ODEs and flows using differential algebraic methods on high-order Taylor series
-
Berz M., Makino K. Verified integration of ODEs and flows using differential algebraic methods on high-order Taylor series. Reliable Computing 1998, 4:361-369.
-
(1998)
Reliable Computing
, vol.4
, pp. 361-369
-
-
Berz, M.1
Makino, K.2
-
5
-
-
33745309007
-
Performance of taylor model methods for validated integration of ODEs
-
Berz M., Makino K. Performance of taylor model methods for validated integration of ODEs. Lecture Notes in Computer Science 2006, 3732:65-74.
-
(2006)
Lecture Notes in Computer Science
, vol.3732
, pp. 65-74
-
-
Berz, M.1
Makino, K.2
-
6
-
-
7444223545
-
A new approach in deterministic global optimization of problems with ordinary differential equations
-
Kluwer Academic Publishers, C.A. Floudas, P.M. Pardalos (Eds.) Frontiers in global optimization
-
Chachuat B., Latifi M.A. A new approach in deterministic global optimization of problems with ordinary differential equations. Nonconvex optimization and its applications 2003, Vol. 74:83-108. Kluwer Academic Publishers. C.A. Floudas, P.M. Pardalos (Eds.).
-
(2003)
Nonconvex optimization and its applications
, vol.74
, pp. 83-108
-
-
Chachuat, B.1
Latifi, M.A.2
-
7
-
-
24944488392
-
Global mixed-integer dynamic optimization
-
Chachuat B., Singer A.B., Barton P.I. Global mixed-integer dynamic optimization. AIChE Journal 2005, 51(8):2235-2253.
-
(2005)
AIChE Journal
, vol.51
, Issue.8
, pp. 2235-2253
-
-
Chachuat, B.1
Singer, A.B.2
Barton, P.I.3
-
9
-
-
0001849172
-
Validating an a priori enclosure using high-order Taylor series
-
Akademie Verlag, Berlin, Germany, G. Alefeld, A. Frommer, B. Lang (Eds.)
-
Corliss G.F., Rihm R. Validating an a priori enclosure using high-order Taylor series. Scientific computing and validated numerics: Proceedings of the international symposium on scientific computing, computer arithmetic and validated numerics - SCAN'95. 1996, 228-238. Akademie Verlag, Berlin, Germany. G. Alefeld, A. Frommer, B. Lang (Eds.).
-
(1996)
Scientific computing and validated numerics: Proceedings of the international symposium on scientific computing, computer arithmetic and validated numerics - SCAN'95.
, pp. 228-238
-
-
Corliss, G.F.1
Rihm, R.2
-
11
-
-
0034102942
-
Global optimization for the parameter estimation of differential-algebraic systems
-
Esposito W.R., Floudas C.A. Global optimization for the parameter estimation of differential-algebraic systems. Industrial and Engineering Chemistry Research 2000, 39(5):1291-1310.
-
(2000)
Industrial and Engineering Chemistry Research
, vol.39
, Issue.5
, pp. 1291-1310
-
-
Esposito, W.R.1
Floudas, C.A.2
-
12
-
-
0003817849
-
-
Kluwer Academic Publishers, Dordrecht, The Netherlands
-
Floudas C.A., Pardalos P.M., Adjiman C.S., Esposito W.R., Gumus Z.H., Harding S.T., Klepeis J.L., Meyer C.A., Schweiger C.A. Handbook of test problems in local and global optimization 1999, Kluwer Academic Publishers, Dordrecht, The Netherlands.
-
(1999)
Handbook of test problems in local and global optimization
-
-
Floudas, C.A.1
Pardalos, P.M.2
Adjiman, C.S.3
Esposito, W.R.4
Gumus, Z.H.5
Harding, S.T.6
Klepeis, J.L.7
Meyer, C.A.8
Schweiger, C.A.9
-
13
-
-
33144466465
-
Dynamic models with uncertain parameters
-
In: X. Avula (Ed.)
-
Harrison, G. W. (1977). Dynamic models with uncertain parameters. In: X. Avula (Ed.), Proc. 1st Intl. Conf. mathematical modeling. Vol. 1 (pp. 295-304).
-
(1977)
Proc. 1st Intl. Conf. mathematical modeling.
, vol.1
, pp. 295-304
-
-
Harrison, G.W.1
-
15
-
-
0036679644
-
Some recent advances in validated methods for IVPs for ODEs
-
Jackson K.R., Nedialkov N.S. Some recent advances in validated methods for IVPs for ODEs. Applied Numerical Mathematics 2002, 42:269-284.
-
(2002)
Applied Numerical Mathematics
, vol.42
, pp. 269-284
-
-
Jackson, K.R.1
Nedialkov, N.S.2
-
16
-
-
35248868105
-
Discussion and empirical comparisons of linear relaxations and alternate techniques in validated deterministic global optimization
-
Kearfott R.B. Discussion and empirical comparisons of linear relaxations and alternate techniques in validated deterministic global optimization. Optimization Methods & Software 2006, 21:715-731.
-
(2006)
Optimization Methods & Software
, vol.21
, pp. 715-731
-
-
Kearfott, R.B.1
-
18
-
-
55549144352
-
Global optimization of linear hybrid systems with varying transition times
-
Lee C.K., Barton P.I. Global optimization of linear hybrid systems with varying transition times. SIAM Journal on Control and Optimization 2008, 47(2):791-816.
-
(2008)
SIAM Journal on Control and Optimization
, vol.47
, Issue.2
, pp. 791-816
-
-
Lee, C.K.1
Barton, P.I.2
-
19
-
-
34047219435
-
Deterministic global optimization of nonlinear dynamic systems
-
Lin Y., Stadtherr M.A. Deterministic global optimization of nonlinear dynamic systems. AIChE Journal 2007, 53(4):866-875.
-
(2007)
AIChE Journal
, vol.53
, Issue.4
, pp. 866-875
-
-
Lin, Y.1
Stadtherr, M.A.2
-
20
-
-
34047210346
-
Validated solutions of initial value problems for parametric ODEs
-
Lin Y., Stadtherr M.A. Validated solutions of initial value problems for parametric ODEs. Applied Numerical Mathematics 2007, 57(10):1145-1162.
-
(2007)
Applied Numerical Mathematics
, vol.57
, Issue.10
, pp. 1145-1162
-
-
Lin, Y.1
Stadtherr, M.A.2
-
21
-
-
0002422258
-
Computation of guaranteed enclosures for the solutions of ordinary initial and boundary value problems
-
Clarendon Press
-
Lohner R.J. Computation of guaranteed enclosures for the solutions of ordinary initial and boundary value problems. Computational ordinary differential equations. 1992, Vol. 1:425-436. Clarendon Press.
-
(1992)
Computational ordinary differential equations.
, vol.1
, pp. 425-436
-
-
Lohner, R.J.1
-
22
-
-
0001847776
-
Efficient control of the dependency problem based on taylor model methods
-
Makino K., Berz M. Efficient control of the dependency problem based on taylor model methods. Reliable Computing 1999, 5(1):3-12.
-
(1999)
Reliable Computing
, vol.5
, Issue.1
, pp. 3-12
-
-
Makino, K.1
Berz, M.2
-
24
-
-
34250381644
-
Computability of global solutions to factorable nonconvex programs: Part I - Convex underestimating problems
-
McCormick G.P. Computability of global solutions to factorable nonconvex programs: Part I - Convex underestimating problems. Mathematical Programming 1976, 10:147-175.
-
(1976)
Mathematical Programming
, vol.10
, pp. 147-175
-
-
McCormick, G.P.1
-
27
-
-
58149389071
-
-
SIAM, Philadelphia, PA
-
Moore R.E., Kearfott R.B., Cloud M.J. Introduction to interval analysis 2009, SIAM, Philadelphia, PA.
-
(2009)
Introduction to interval analysis
-
-
Moore, R.E.1
Kearfott, R.B.2
Cloud, M.J.3
-
29
-
-
0035724114
-
An effective high-order interval method for validating existence and uniqueness of the solution of an IVP for an ODE
-
Nedialkov N.S., Jackson K.R., Pryce J.D. An effective high-order interval method for validating existence and uniqueness of the solution of an IVP for an ODE. Reliable Computing 2001, 7:449-465.
-
(2001)
Reliable Computing
, vol.7
, pp. 449-465
-
-
Nedialkov, N.S.1
Jackson, K.R.2
Pryce, J.D.3
-
31
-
-
0037292825
-
Taylor forms - Use and limits
-
Neumaier A. Taylor forms - Use and limits. Reliable Computing 2002, 9(1):43-79.
-
(2002)
Reliable Computing
, vol.9
, Issue.1
, pp. 43-79
-
-
Neumaier, A.1
-
32
-
-
31244435059
-
A rigorous global optimization algorithm for problems with ordinary differential equations
-
Papamichail I., Adjiman C.S. A rigorous global optimization algorithm for problems with ordinary differential equations. Journal of Global Optimization 2002, 24:1-33.
-
(2002)
Journal of Global Optimization
, vol.24
, pp. 1-33
-
-
Papamichail, I.1
Adjiman, C.S.2
-
33
-
-
70350344688
-
A hybrid bounding method for computing an over-approximation for the reachable set of uncertain nonlinear systems
-
Ramdani N., Meslem N., Candau Y. A hybrid bounding method for computing an over-approximation for the reachable set of uncertain nonlinear systems. IEEE Transactions on Automatic Control 2009, 54(10):2352-2364.
-
(2009)
IEEE Transactions on Automatic Control
, vol.54
, Issue.10
, pp. 2352-2364
-
-
Ramdani, N.1
Meslem, N.2
Candau, Y.3
-
35
-
-
0005675076
-
On a class of enclosure methods for initial value problems
-
Rihm R. On a class of enclosure methods for initial value problems. Computing 1994, 53:369-377.
-
(1994)
Computing
, vol.53
, pp. 369-377
-
-
Rihm, R.1
-
36
-
-
79953779034
-
Discretize-then-relax approach for convex/concave relaxations of the solutions of parametric ODEs
-
in press, doi:10.1016/j.apnum.2011.01.009
-
Sahlodin A., Chachuat B. Discretize-then-relax approach for convex/concave relaxations of the solutions of parametric ODEs. Applied Numerical Mathematics 2010, in press, doi:10.1016/j.apnum.2011.01.009.
-
(2010)
Applied Numerical Mathematics
-
-
Sahlodin, A.1
Chachuat, B.2
-
37
-
-
77950371059
-
Tight, efficient bounds on the solutions of chemical kinetics models
-
Scott J.K., Barton P.I. Tight, efficient bounds on the solutions of chemical kinetics models. Computers and Chemical Engineering 2010, 34(5):717-731.
-
(2010)
Computers and Chemical Engineering
, vol.34
, Issue.5
, pp. 717-731
-
-
Scott, J.K.1
Barton, P.I.2
-
39
-
-
83555172534
-
Generalized McCormick relaxations
-
in press, doi:10.1007/s10898-011-9664-7
-
Scott, J. K., Stuber, M. D., Barton, P. I. (2010). Generalized McCormick relaxations. Journal of Global Optimization; in press, doi:10.1007/s10898-011-9664-7.
-
(2010)
Journal of Global Optimization
-
-
Scott, J.K.1
Stuber, M.D.2
Barton, P.I.3
-
40
-
-
33751231736
-
Bounding the solutions of parameter dependent nonlinear ordinary differential equations
-
Singer A.B., Barton P.I. Bounding the solutions of parameter dependent nonlinear ordinary differential equations. SIAM Journal on Scientific Computing 2006, 27(6):2167-2182.
-
(2006)
SIAM Journal on Scientific Computing
, vol.27
, Issue.6
, pp. 2167-2182
-
-
Singer, A.B.1
Barton, P.I.2
-
41
-
-
33144473448
-
Global optimization with nonlinear ordinary differential equations
-
Singer A.B., Barton P.I. Global optimization with nonlinear ordinary differential equations. Journal of Global Optimization 2006, 34(2):159-190.
-
(2006)
Journal of Global Optimization
, vol.34
, Issue.2
, pp. 159-190
-
-
Singer, A.B.1
Barton, P.I.2
-
42
-
-
0033134718
-
A symbolic reformulation/spatial branch-and-bound algorithm for the global optimisation of nonconvex MINLPs
-
Smith E.M.B., Pantelides C.C. A symbolic reformulation/spatial branch-and-bound algorithm for the global optimisation of nonconvex MINLPs. Computers and Chemical Engineering 1999, 23:457-478.
-
(1999)
Computers and Chemical Engineering
, vol.23
, pp. 457-478
-
-
Smith, E.M.B.1
Pantelides, C.C.2
-
43
-
-
0038292297
-
-
Kluwer Academic Publishers, Boston, MA
-
Tawarmalani M., Sahinidis N.V. Convexification and global optimization in continuous and mixed-integer nonlinear programming: Theory, algorithms, software, and applications. Nonconvex optimization and its applications 2002, Kluwer Academic Publishers, Boston, MA.
-
(2002)
Convexification and global optimization in continuous and mixed-integer nonlinear programming: Theory, algorithms, software, and applications. Nonconvex optimization and its applications
-
-
Tawarmalani, M.1
Sahinidis, N.V.2
|